Proceedings of the Centre for Mathematics and its Applications

Flow of hypersurfaces by curvature functions

Ben Andrews

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Abstract

This seminar concerns a class of flow equations for immersed hypersurfaces, modelled on the well-known mean curvature flow. The flows in this class share much of the qualitative behaviour of the mean curvature flow, but are in general fully nonlinear; this compiicates some parts of their analysis. Other calculations are clarified by the general setting. I will present some results on the behaviour of convex hypersurfaces under these flows, which extend work on specific flows by Huisken (Hul), Tso (Tl) and Chow (Cl-2). Also new is a Harnack inequality for solutions of very general flows; this generalises results of Hamilton (Hal) and Chow (C3). Flows of this kind have some applications in geometry; for such purposes the mean curvature flow is not always the best candidate - I will describe an example which applies to manifolds of non-negative sectional curvature.

Article information

Source
Theoretical and Numerical Aspects of Geometric Variational Problems. Gerd Dziuk, Gerhard Huisken, and John Hutchinson, eds. Proceedings of the Centre for Mathematics and its Applications, v. 26. (Canberra AUS: Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, 1991), Ben-Andrews

Dates
First available in Project Euclid: 18 November 2014

Permanent link to this document
https://projecteuclid.org/ euclid.pcma/1416323549

Mathematical Reviews number (MathSciNet)
MR1139026

Zentralblatt MATH identifier
0758.53028

Citation

Andrews, Ben. Flow of hypersurfaces by curvature functions. Theoretical and Numerical Aspects of Geometric Variational Problems, Ben--Andrews, Centre for Mathematics and its Applications, Mathematical Sciences Institute, The Australian National University, Canberra AUS, 1991. https://projecteuclid.org/euclid.pcma/1416323549


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